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Article Dans Une Revue Journal of Geometry and Physics Année : 2015

Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds

Résumé

We introduce a simple and very fast algorithm that computes Weil-Petersson metrics on moduli spaces of polarized Calabi-Yau manifolds. Also, by using Donaldson's quantization link between the infinite and finite dimensional G.I.T quotients that describe moduli spaces of varieties, we define a natural sequence of Kaehler metrics. We prove that the sequence converges to the Weil-Petersson metric. We also develop an algorithm that numerically approximates such metrics, and hence the Weil-Petersson metric itself. Explicit examples are provided on a family of Calabi-Yau Quintic hypersurfaces in CP^4. The scope of our second algorithm is much broader; the same techniques can be used to approximate metrics on null spaces of Dirac operators coupled to Hermite Yang-Mills connections.

Dates et versions

hal-01282380 , version 1 (03-03-2016)

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Citer

Julien Keller, Sergio Lukic. Numerical Weil-Petersson metrics on moduli spaces of Calabi-Yau manifolds. Journal of Geometry and Physics, 2015, 92, ⟨10.1016/j.geomphys.2015.02.018⟩. ⟨hal-01282380⟩
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